Question

Quarter	Year 1	Year 2	Year 3
1	3	6	8
2	2	4	8
3	4	7	9
4	6	9	11

(b)	Use a multiple regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data. Qtr1 = 1 if Quarter 1, 0 otherwise; Qtr2 = 1 if Quarter 2, 0 otherwise; Qtr3 = 1 if Quarter 3, 0 otherwise.
	If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) If the constant is "1" it must be entered in the box. Do not round intermediate calculation.
	ŷ =  +___  Qtr1 + ___ Qtr2 + ___ Qtr3

Compute the quarterly forecasts for next year based on the model you developed in part (b).
	If required, round your answers to three decimal places. Do not round intermediate calculation.
	Year Quarter Ft 4 1 4 2 4 3 4 4

Use a multiple regression model to develop an equation to account for trend and seasonal effects in the data. Use the dummy variables you developed in part (b) to capture seasonal effects and create a variable t such that t = 1 for Quarter 1 in Year 1, t = 2 for Quarter 2 in Year 1,… t = 12 for Quarter 4 in Year 3.
	If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
	ŷ =  + __ Qtr1 +__  Qtr2 +__  Qtr3 +___  t

Compute the quarterly forecasts for next year based on the model you developed in part (d). Do not round your interim computations and round your final answer to three decimal places. Year Quarter Period Ft 4 1 13 4 2 14 4 3 15 4 4 16

Is the model you developed in part (b) or the model you developed in part (d) more effective?
	If required, round your intermediate calculations and final answer to three decimal places.
	Model developed in part (b) Model developed in part (d) MSE

Answer 1

b)

DATA

y	t	Q1	Q2	Q3
3	1	1	0	0
2	2	0	1	0
4	3	0	0	1
6	4	0	0	0
6	5	1	0	0
4	6	0	1	0
7	7	0	0	1
9	8	0	0	0
8	9	1	0	0
8	10	0	1	0
9	11	0	0	1
11	12	0	0	0

Excel result

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.562657013
R Square	0.316582915
Adjusted R Square	0.060301508
Standard Error	2.661453237
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	3	26.25	8.75	1.235294	0.358901
Residual	8	56.66666667	7.083333333
Total	11	82.91666667
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	8.667	1.536590743	5.640191903	0.000487	5.123282
Q1	-3	2.173067468	-1.38053698	0.204764	-8.0111
Q2	-4	2.173067468	-1.840715973	0.102932	-9.0111
Q3	-2	2.173067468	-0.920357987	0.384298	-7.0111

y^= 8.667 - 3 Q1 -4 Q2 -2 Q3

c)

Year	Quarter	Ft
4	1	5.667
4	2	4.667
4	3	6.667
4	4	8.667

d)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.990659899
R Square	0.981407035
Adjusted R Square	0.970782484
Standard Error	0.469295318
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	4	81.375	20.34375	92.37162	3.89E-06
Residual	7	1.541666667	0.220238095
Total	11	82.91666667
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	3.417	0.428406053	7.975299706	9.3E-05	2.403647
t	0.656	0.041480238	15.82078687	9.77E-07	0.558165
Q1	-1.031	0.402878254	-2.559706285	0.037568	-1.98391
Q2	-2.688	0.392055911	-6.854889634	0.000241	-3.61456
Q3	-1.344	0.385416667	-3.486486486	0.010177	-2.25512

y^= 3.417 -1.013 Q1 -2.688 Q2 -1.344 Q3 + 0.656 t

e)

Year	Quarter	Period	Ft
4	1	13	10.917
4	2	14	9.917
4	3	15	11.917
4	4	16	13.917